Information about materials is essential in component and system design. For example, components and systems designed in automotive, aerospace, and microelectronics applications require many different types of materials. Component and systems designers need to have information about the materials in order to select one or more materials that will provide the required performance.
A designer may select a material for use in a component based on one or more design requirements. The designer typically has an in-depth understanding of materials, and is capable of making an appropriate material selection based on the design requirements.
Simulation-Based Engineering
Computer-based physical models are often used in component and systems design to investigate design performance. A physical model requires a geometric representation, a definition of physical loads, a mathematical model of the material response, and model parameters that represent a specific material in the model. The execution of the physical model requires a simulation code which processes the above data and produces a physical simulation of a real event. For example, a physical model of an automobile can be processed in a simulation code to simulate a collision. Physical models are very useful tools in component and systems design as, in most cases, they can be produced more quickly and economically then an actual prototype.
FIG. 1 illustrates a conventional simulation-based design of a component. In this simulation-based design, H-11 tool steel, which is a specific type of steel, is used within the context of a Power Law Hardening (PLH) material model.
The simulation-based design begins with a finite element model 104 of the component. The finite element model 104 is one form of a physical model of a component. In a finite element model, the geometry usually originates from a computer aided design (CAD) model.
Next, the finite element model 104 is discretized into regular-shaped elements, called the discretized finite element model 108. The discretized finite element model 108 is represented by one or more mathematical equations.
Next, a simulation code, called a finite element analysis (FEA) code 112, is used to solve the mathematical equations of the discretized finite element model 108. The FEA code 112 is provided with applied loads, boundary conditions and model parameters. The FEA code 112 produces a simulation of the component in response to applied loads, boundary conditions and model parameters. The graph 116 is the simulation result produced by the FEA code 112. The parameters, A and n, shown are specific model parameters that represent H-11 tool steel within the context of a Power Law Hardening (PLH) material model. Using this physical model, a designer can iterate on design details, such as, for example, component geometry or material selection, until the design produces desirable results.
The application of physical models to system and component design is referred to herein as simulation-based engineering. In addition to finite element models, there are many other types of physical models including ‘meshless’ models that are based on a solid model geometry. The common characteristic of these physical models is that they mathematically represent material response.
The physical models used in simulation-based engineering processes are valuable information assets throughout a product's lifecycle. After a product has been placed in service, a need may arise to reconsider the materials used in the product. There may be a need for a redesign due to an upgrade or modernization of the product or a change in design requirements. There may also be a need for a redesign due to a significant finding investigation. For example, a specific model of a vehicle may be subjected to an investigation following a series of accidents. The investigation may reveal defects associated with one or more components in that vehicle. The entire vehicle model-line may be recalled, and redesign of one or more components may be necessary.
In the above scenario, the original design intent is necessary to determine why a specific material was used in a component. The original design intent is considered a valuable information asset during redesign. Without knowledge of why a designer originally selected the material, it is difficult to select a replacement that will fulfill the new requirements. If the information about the original design intent is lost, the designer will lack important information necessary for a suitable redesign.
The difficulty in identifying material specifications becomes an issue when a component or a system becomes the subject of a modeling study. It may take a considerable amount of time to identify all of the materials in a component or a system.
Constitutive Models
The mathematical model of a material response is referred to as a constitutive model. A constitutive model is a mathematical representation of an ideal material response mode. The constitutive model approximates physical observations of a real material's response over a suitably restricted range. In general, a constitutive model is specific to particular class of material. For example, a plasticity model such as the Power Law Hardening (PLH) model mathematically represents large deformation response beyond the yield strength of a material. Although the PLH model is not specific to any material, in general it produces a good match to the response of metals.
A model parameter is a numeric constant associated with a constitutive model. A constitutive model may include one or more model parameters. A property set is a complete set of model parameters required to numerically model the response of a particular material. The property set for a particular species of material is generally obtained through some estimation process that requires test data.
The constitutive models used in physical models have been developed over time and are based on classical theories of material modeling. A significant number of constitutive models exist and are well documented in literature, and are usually in the form of complex mathematical theories. New constitutive models continue to be developed to address specific needs in component and system design.
A numerical implementation of a constitutive model must be created for it to be integrated into a simulation code. The numerical implementation of a constitutive model is an approximation of a mathematical theory. This is necessary because a constitutive model often requires a numerical approximation of complex mathematical theory, such as an integral equation with no exact solution. Most simulation codes contain a library of constitutive models to handle a wide variety of materials and load conditions.
In order to develop a numerical implementation of a constitutive model, a predicted material response is compared to the response of a constitutive model. The constitutive model's equations are adjusted until the model produces a good match to test data for a variety of materials and load conditions.
Material Model Driver
A material model driver (MMD) is a specialized computer code that can drive the numerical implementation of a constitutive model over a user prescribed load path. When implemented in a simulation code, a numerical implementation of a constitutive model can simulate the model response for a complex three-dimensional geometry. The finite element model illustrated in FIG. 1 is composed of many elements or cells that represent such a complex geometry. For the purposes of validating model performance, it is useful to be able to drive the model in a single cell. This removes geometry complexities and allows the constitutive modeler to focus on the model response over a well-defined load. The MMD is specific to a constitutive model and is usually a simplified version of the three-dimensional model contained in the simulation code. The MMD is generally used in the initial stages of modeling and numerical implementation. It is also used in subsequent parameter estimation algorithms.
Materials Characterization Tests
Materials characterization tests are specialized tests performed to produce the material response represented by the constitutive model. These tests are performed on a material sample of specific shape and under loads within the load-range of interest. The material response as a function of the applied load is measured and recorded. One or more types of materials characterization tests may be necessary for characterizing a given material in the context of a given constitutive model. The materials characterization tests are required to perform parameter estimations for a given material and a given model.
An example of a materials characterization test is a ‘uniaxial tensile test’ performed to characterize the elastic-plastic response of a metal. A small cylindrical sample of the metal is strain-loaded in an axial direction until it breaks. A one-dimensional load-displacement response is recorded in a stress-versus-strain plot. Within the context of several plasticity models, this test is sufficient for characterizing the material response of a given metal with a continuously increasing load. If the designer wants to simulate a cyclical load or a reverse load, then a materials characterization test that produces this response is needed.
Parameter Estimation
A parameter estimation is the process of calculating a property set for a given material species in the context of a constitutive model given a set of materials characterization tests performed on that material. The end product of this process is a property set that can be used in a physical model to represent a particular type of material in the context of the constitutive model.
The parameter estimation process is typically an iterative one. The loads applied during the tests are applied to the model and the model response is compared to the test response. The parameters are changed until the model response closely matches that of the test data. A variety of numerical optimization methods have been developed that automate the parameter estimation process.
The constitutive models, materials characterization test data, parameter estimation processes, model parameters and property sets representing specific materials are all valuable information assets of simulation-based engineering. Efficient management and preservation of these assets is essential, as their generation typically requires a considerable investment in material testing, material model development and physical simulations. At present there is a need for an application that provides efficient management and preservation of these assets. There is a need for an application that provides a single point of access for designers and analysts to retrieve validated constitutive models, model parameters, materials characterization test data and other assets discussed above. There is a need for an application that provides information to ensure traceability back to test data. There is a need for a collaborative application to support end-to-end data acquisition process. There are is a need for an application to capture and reproduce the parameter estimation process for developed models. There is a need for an application that compares model property sets to material characterization tests, providing greater confidence in their use. There is a need for an application that allows exploratory development of new constitutive models.